Question

Решить систему уравнений

Answer 1

$left { {{ frac{1}{x+y}- frac{6}{x-y} =-2} atop {frac{1}{x+y}+ frac{3}{x-y} = frac{1}{4} }} right. \ \ x neq y \ x neq -y$
отнимем
$frac{3}{x-y}+frac{6}{x-y} = frac{1}{4} +2 \ \ frac{9}{x-y} = frac{9}{4} \ \ x-y=4 \ \ x=4+y \ \ frac{1}{4+y+y} - frac{6}{4+y-y} =-2 \ \ frac{1}{4+2y} =- frac{1}{2} \ \ 2y=-6 \ \ y=-3 \ \ x=4-3=1 \ \ OTVET: (1;-3)$